Question

Parallelogram WXYZ is a rectangle . The length of side WX = 4x + 10, the length of side XY = 2x - 6 and the perimeter of WXYZ = 116. What is the length of side WX?​

Answer 1

Using the charasteristics of a parallelogram, the length of line segment MX is 8 in (Third option).

Explanation:

In parallelogram WXYZ:

WY=12 in., this is a diagonal in the parallelogram

XZ=16 in., this is the other diagonal in the parallelogram

WX=10 in., this is one of the sides of the parallelogram

XY=9 in., this is the other side of the parallelogram

MX=? this segment is between the vertex X and the point of intersection of the diagonals

In a parallelogram the diagonals intersect (point M) dividing them in equal parts each other, then:

MX=MZ=XZ/2

MX=MZ=(16 in.)/2

MX=MZ=8 in.

Answer 2

Answer: WX = 46

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Work Shown:

Length = L = WX = 4x+10

Height = H = XY = 2x-6

P = Perimeter of rectangle = 116

P = 2*(L+H)

2(L+H) = 116

2(4x+10+2x-6) = 116

2(6x+4) = 116

6x+4 = 116/2

6x+4 = 58

6x = 58-4

6x = 54

x = 54/6

x = 9

Using this x value, we find that,

WX = 4x+10 = 4*9+10 = 36+10 = 46

We can also see that

XY = 2x-6 = 2*9-6 = 18-6 = 12

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The length and height of this rectangle are L = 46 and H = 12

This leads to the perimeter of...

P = 2*(L+H)

P = 2*(46+12)

P = 2*(58)

P = 116

This confirms the answer.